r = 0.437*2/3
xdim3 = [a,b,r]
n_i_1 = [1]
m_i_1 = [1]
lam1 = Laminate(n_i_1, m_i_1, matLib)
# Organize the laminates into an array
laminates_Lay3 = [lam1]
af3 = Airfoil(1.,name='NACA2412')
# Create the cross-section object and mesh it
xsect_Lay3 = XSect(4,af3,xdim3,laminates_Lay3,matLib,typeXSect='rectHole',nelem=40)
# Run the cross-sectional analysis. Since this is an airfoil and for this,
# symmetric airfoils the AC is at the 1/c chord, we will put the reference axis
# here
xsect_Lay3.xSectionAnalysis()#ref_ax=[0.25*c3,0.])
# Let's see what the rigid cross-section looks like:
xsect_Lay3.plotRigid()
# Print the stiffness matrix
xsect_Lay3.printSummary(stiffMat=True)
force3 = np.array([0.,0.,0.,0.,0.,216.])
# Calculate the force resultant effects
xsect_Lay3.calcWarpEffects(force=force3)
# This time let's plot the max principle stress:
xsect_Lay3.plotWarped(figName='sigma_xz',\
warpScale=10,contour='sig_13',colorbar=True)
xsect_Lay3.plotWarped(figName='sigma_yz',\
warpScale=10,contour='sig_23',colorbar=True)
xsect_Lay3.plotWarped(figName='RSS Shear',\
warpScale=10,contour='rss_shear',colorbar=True)
xsect_Lay3.plotWarped(figName='Axial Stress',\
warpScale=10,contour='sig_33',colorbar=True)
xsect_Lay3 = XSect(4,af3,xdim3,laminates_Lay3,matLib,typeXSect='box',meshSize=2)
# Run the cross-sectional analysis. Since this is an airfoil and for this,
# symmetric airfoils the AC is at the 1/c chord, we will put the reference axis
# here
xsect_Lay3.xSectionAnalysis(ref_ax=[0.25*c3,0.])
# Let's see what the rigid cross-section looks like:
xsect_Lay3.plotRigid()
# Print the stiffness matrix
xsect_Lay3.printSummary(stiffMat=True)
# Create an applied force vector. For a wing shape such as this, let's apply a
# semi-realistic set of loads:
force3 = np.array([10.,100.,0.,10.,1.,0.])
# Calculate the force resultant effects
xsect_Lay3.calcWarpEffects(force=force3)
# This time let's plot the max principle stress:
xsect_Lay3.plotWarped(figName='NACA2412 Box Beam Max Principle Stress',\
warpScale=10,contour='MaxPrin',colorbar=True)
# Establish Matricies
A = xsect_Lay3.A
R = xsect_Lay3.R
E = xsect_Lay3.E
C = xsect_Lay3.C
L = xsect_Lay3.L
M = xsect_Lay3.M
D = xsect_Lay3.D
Z6 = np.zeros((6,6))
nd = 3*len(xsect_Lay3.nodeDict)
Tr = np.zeros((6,6));Tr[0,4] = -1;Tr[1,3] = 1
@profile
def luDecomp():
''' lam1.printSummary() lam2.printSummary() lam3.printSummary() lam4.printSummary() laminates_Lay3 = [lam1,lam2,lam3,lam4] xsect_Lay3 = XSect(4,af2,xdim2,laminates_Lay3,matLib,typeXSect='rectBox',meshSize=1.87) xsect_Lay3.xSectionAnalysis() xsect_Lay3.printSummary(stiffMat=True) xsect_Lay3.calcWarpEffects(force=force) #import mayavi.mlab as mlab #xsect_Lay3.plotWarped(figName='Stress sig_11',warpScale=1,contLim=[-500,500],contour='sig_11') xsect_Lay3.plotWarped(figName='Stress sig_11',warpScale=0,contour='sig_11') #xsect_Lay3.plotRigid(figName='Stress sig_11') #mlab.colorbar() #xsect_Lay3.plotWarped(figName='Stress sig_22',warpScale=1,contLim=[-5075,9365],contour='sig_22') xsect_Lay3.plotWarped(figName='Stress sig_22',warpScale=0,contour='sig_22') #mlab.colorbar() #xsect_Lay3.plotWarped(figName='Stress sig_33',warpScale=1,contLim=[25762,293000],contour='sig_33') xsect_Lay3.plotWarped(figName='Stress sig_33',warpScale=0,contour='sig_33') #mlab.colorbar() #xsect_Lay3.plotWarped(figName='Stress sig_12',warpScale=1,contLim=[-2932,3116],contour='sig_12') xsect_Lay3.plotWarped(figName='Stress sig_12',warpScale=0,contour='sig_12') #mlab.colorbar()
# stiffnesses, ect.
xsect1.printSummary(stiffMat=True)
# Notice that from the command line output, all of the important cross-
# sectional geometric properties are located at the origin. By observing the
# cross-section stiffness matrix, it can be seen by the 1,3 entry that there
# is shear-axial coupling. From the non-zero 4,6 entry, we can also tell that
# the cross-section has bending-torsion coupling.
# We can apply a force to the face of this cross-section at the reference axis
# (which in this case is at x,y = 0,0) and see what the stresses look like. In
# this case we'll apply [Fx,Fy,Fz,Mx,My,Mz]=[0.,0.,0.,100.,0.,0.] as if the
# beam belonging to this cross-section were in pure bending.
force1 = np.array([0., 100., 0., 10., 0., 0.])
xsect1.calcWarpEffects(force=force1)
# Having applied the force, let's see what the sigma_zz (normal stresses of the
# beam) look like
xsect1.plotWarped(figName='Laminate Sigma_33 Stress',warpScale=10,\
contour='sig_33',colorbar=True)
# Let's look at the sigma_13 stress state now since we know there is torsion
# coupling:
xsect1.plotWarped(figName='Laminate Sigma_13 Stress',warpScale=10,\
contour='sig_13',colorbar=True)
# Notice the increased stress in two of the plies? Recall which ones those are?
# Those plies are the 45 degree plies which are currently taking the shear!
# CREATE A LAMIANTE CROSS-SECTION WITH A DIFFERENT REFERENCE AXIS
# ===============================================================
# The cross-section we just made happened to have all of it's geometrical
# locations (mass center, shear center, tension center) at the origin, which
# is where we applied our force resultant. Suppose we wanted to give the cross-
# section a different reference axis. We can do this by executing the
# xSectionAnalysis method again:
ref_ax = [.5, 0.]
# stiffnesses, ect.
xsect1.printSummary(stiffMat=True)
# Notice that from the command line output, all of the important cross-
# sectional geometric properties are located at the origin. By observing the
# cross-section stiffness matrix, it can be seen by the 1,3 entry that there
# is shear-axial coupling. From the non-zero 4,6 entry, we can also tell that
# the cross-section has bending-torsion coupling.
# We can apply a force to the face of this cross-section at the reference axis
# (which in this case is at x,y = 0,0) and see what the stresses look like. In
# this case we'll apply [Fx,Fy,Fz,Mx,My,Mz]=[0.,0.,0.,100.,0.,0.] as if the
# beam belonging to this cross-section were in pure bending.
force1 = np.array([0.,100.,0.,10.,0.,0.])
xsect1.calcWarpEffects(force=force1)
# Having applied the force, let's see what the sigma_zz (normal stresses of the
# beam) look like
xsect1.plotWarped(figName='Laminate Sigma_33 Stress',warpScale=10,\
contour='sig_33',colorbar=True)
# Let's look at the sigma_13 stress state now since we know there is torsion
# coupling:
xsect1.plotWarped(figName='Laminate Sigma_13 Stress',warpScale=10,\
contour='sig_13',colorbar=True)
# Notice the increased stress in two of the plies? Recall which ones those are?
# Those plies are the 45 degree plies which are currently taking the shear!
# CREATE A LAMIANTE CROSS-SECTION WITH A DIFFERENT REFERENCE AXIS
# ===============================================================
# The cross-section we just made happened to have all of it's geometrical
# locations (mass center, shear center, tension center) at the origin, which
# is where we applied our force resultant. Suppose we wanted to give the cross-
# section a different reference axis. We can do this by executing the
# xSectionAnalysis method again:
ref_ax = [.5,0.]
meshSize=2)
# Run the cross-sectional analysis. Since this is an airfoil and for this,
# symmetric airfoils the AC is at the 1/c chord, we will put the reference axis
# here
xsect_Lay3.xSectionAnalysis(ref_ax=[0.25 * c3, 0.])
# Let's see what the rigid cross-section looks like:
xsect_Lay3.plotRigid()
# Print the stiffness matrix
xsect_Lay3.printSummary(stiffMat=True)
# Create an applied force vector. For a wing shape such as this, let's apply a
# semi-realistic set of loads:
force3 = np.array([10., 100., 0., 10., 1., 0.])
# Calculate the force resultant effects
xsect_Lay3.calcWarpEffects(force=force3)
# This time let's plot the max principle stress:
xsect_Lay3.plotWarped(figName='NACA2412 Box Beam Max Principle Stress',\
warpScale=10,contour='MaxPrin',colorbar=True)
# Establish Matricies
A = xsect_Lay3.A
R = xsect_Lay3.R
E = xsect_Lay3.E
C = xsect_Lay3.C
L = xsect_Lay3.L
M = xsect_Lay3.M
D = xsect_Lay3.D
Z6 = np.zeros((6, 6))
nd = 3 * len(xsect_Lay3.nodeDict)
Tr = np.zeros((6, 6))
Tr[0, 4] = -1
Tr[1, 3] = 1
laminates_Lay3 = [lam1]
af3 = Airfoil(1., name='NACA2412')
# Create the cross-section object and mesh it
xsect_Lay3 = XSect(4,
af3,
xdim3,
laminates_Lay3,
matLib,
typeXSect='rectHole',
nelem=40)
# Run the cross-sectional analysis. Since this is an airfoil and for this,
# symmetric airfoils the AC is at the 1/c chord, we will put the reference axis
# here
xsect_Lay3.xSectionAnalysis() #ref_ax=[0.25*c3,0.])
# Let's see what the rigid cross-section looks like:
xsect_Lay3.plotRigid()
# Print the stiffness matrix
xsect_Lay3.printSummary(stiffMat=True)
force3 = np.array([0., 0., 0., 0., 0., 216.])
# Calculate the force resultant effects
xsect_Lay3.calcWarpEffects(force=force3)
# This time let's plot the max principle stress:
xsect_Lay3.plotWarped(figName='sigma_xz',\
warpScale=10,contour='sig_13',colorbar=True)
xsect_Lay3.plotWarped(figName='sigma_yz',\
warpScale=10,contour='sig_23',colorbar=True)
xsect_Lay3.plotWarped(figName='RSS Shear',\
warpScale=10,contour='rss_shear',colorbar=True)
xsect_Lay3.plotWarped(figName='Axial Stress',\
warpScale=10,contour='sig_33',colorbar=True)
